What are (Not) Theories & Models?

Felix Schönbrodt

Ludwig-Maximilians-Universität München

2023-10-27

What is a theory?

Like so many words that are bandied about, the word theory threatens to become meaningless. Because its referents are so diverse - including everything from minor working hypotheses, through comprehensive but vague and unordered speculations,to axiomatic systems of thought - use of the word often obscures rather than creates understanding.
Merton (1967, p. 39)

Maybe an easier question for the start: But what is not a theory?

What is not a theory? 1

(Note: While these features of a scholarly article do not constitute a theory, they might be important in their own right)

  1. References Are Not Theory

A manuscript that Robert Sutton edited had strong data, but all three reviewers emphasized that it had “weak theory” and “poorly motivated hypotheses.” The author responded to these concerns by writing a new introduction that added citations to many papers containing theory and many terms like “psycho-social theory,” “identity theory,” and “social comparison theory.”

But it still contained no discussion of what these theories were about and no discussion of the logical arguments why these theories led to the author’s predictions. The result was that this paper contained almost no theory, despite the author’s assertion that much had been added.

Solution:

Authors need to explicate which concepts and causal arguments are adopted from cited sources and how they are linked to the theory being developed or tested.

What is not a theory? 2

  1. Data Are Not Theory

Empirical evidence plays an important role in confirming, revising, or discrediting existing theory and in guiding the development of new theory. But observed patterns like beta weights, factor loadings, or consistent statements by informants rarely constitute causal explanations.

Kaplan (1964) asserted that theory and data each play a distinct role in behavioral science research: Data describe which empirical patterns were observed and theory explains why empirical patterns were observed or are expected to be observed.

Also: Theories do not explain data - theories explain phenomena!

What is not a theory? 3

  1. Lists of Variables or Constructs Are Not Theory

Papers […] often are written as if well-defined variables or constructs, by themselves, are enough to make theory. Sometimes the list of variables represents a logical attempt to cover all or most of the determinants of a given outcome or process.

Such lists may be useful catalogs of variables that can be entered as predictors or controls in multiple regression equations […], but they do not constitute theory.

Lists of constructs (without an explicit definition of their causal relationship) often are called a framework.

What is not a theory? 4

  1. Diagrams (Alone) Are Not Theory

This is an extension of (3) “List of constructs”: Put each construct that you deem relevant into a box and draw arrows between all constructs (because in a complex system everything is connected with everything)

What is not a theory? 4

Figure 1. Holistic wellbeing model for school education.

What is not a theory? 4

What is not a theory? 4

What is not a theory? 4

  1. Diagrams (Alone) Are Not Theory

Diagrams or figures can be a valuable part of a research paper but also, by themselves, rarely constitute theory. […]

More helpful are figures that show causal relationships in a logical ordering, so that readers can see a chain of causation or how a third variable intervenes in or moderates a relationship. Also useful are temporal diagrams showing how a particular process unfolds over time. […]

As Whetten (1989) suggested, while boxes and arrows can add order to a conception by explicitly delineating patterns and causal connections, they rarely explain why the proposed connections will be observed. Some verbal explication is almost always necessary.

What is not a theory? 5

  1. Hypotheses (or Predictions) Are Not Theory.

Hypotheses can be an important part of a well-crafted conceptual argument. They serve as crucial bridges between theory and data, making explicit how the variables and relationships that follow from a logical argument will be operationalized. […]

Hypotheses do not (and should not) contain logical arguments about why empirical relationships are expected to occur. Hypotheses are concise statements about what is expected to occur, not why it is expected to occur.

But, then:
What is a theory?

Theories as causal explanations

“It may be said… that an explanation is not fully adequate unless its explanans, if taken account of in time, could have served as a basis for predicting the phenomenon under consideration…

It is this potential predictive force which gives scientific explanation its importance: Only to the extent that we are able to explain empirical facts can we attain the major objective of scientific research, namely not merely to record the phenomena of our experience, but to learn from them, by basing upon them theoretical generalizations which enable us to anticipate new occurrences and to control, at least to some extent, the changes in our environment
 Hempel & Oppenheim, 1948, (p. 138)

TCM: A methodology for constructing theories

%%{
  init: {
    'theme': 'base',
    'flowchart': { 'curve': 'natural' }
  }
}%%
flowchart LR
  T(Theory)
  P(Phenomena)
  D(Data)
  
  T -- "Explanation" --> P
  P -- "Abduction" --> T
  P -- "Prediction" --> D
  D -- "Generalization" --> P

Phenomena: Stable and general features of the world in need of explanation. Can be understood as robust generalizations of patterns in empirical data. They are the explanatory targets for scientific theories (the explanandum). In psychology often called “effects”.

Data: Relatively direct observations. Refer to particular empirical patterns in concrete data sets rather than empirical generalizations (which would be phenomenona).

Explanatory Theories are constructed to explain the empirical phenomena that are evidenced by data (i.e., they are the explanans). Explanatory theories can be expressed in terms of a set of linked propositions referring to latent psychological constructs. At least one of these propositions expresses a general principle.

“theory T putatively explains phenomenon P” means “if the world were as T says it is, P would follow as a matter of course.” Although this notion of explanation is arguably incomplete, it has the advantages of being close to the commonsense understanding of the concept and being easy to implement in a formal model—namely by creating a virtual world in which theory T is true and showing that this world will indeed produce phenomenon P.

Definitions (1)

What is an (explanatory) theory?

A theory is a set of statements about the relationship(s) between two or more constructs with a nomological (i.e. law-like) character. (explanans)

What is a formal/mathematical/computational model?

A {formal|mathematical|computational} model is a precise, mathematical representation of the theory’s principles and relationships. It serves as a bridge between abstract theoretical principles and the empirical world.

Sometimes a theory is so highly formalized that it is virtually identical to a model of it. But more often, there is a gap between theory and implemented models: We need more assumptions to implement a model in computer code. In this case, multiple models can satisfy the axioms and constraints of a theory (see next slide).

Formal models: One possible implementation

What is a formal/mathematical/computational model?

In a nutshell

A model is a function that transforms input variables into an output variable (the dependent variable).

Type of input variables:

  • Fixed parameters: Parameters that are chosen a priori and do not change in the light of empirical data. Their values are based on previous research, theory, or external information (such as properties of the world).
  • Free parameters: Can be adjusted to optimize the fit of the model to data. They are estimated from empirical data.
  • Nuisance parameters:

Exercise (15 min): Apply to your Buridan model

List all parameters that you have in your model. Sort them into fixed and free parameters.

Definitions (2)

What is an (explanatory) theory?

A theory is a set of statements about the relationship(s) between two or more constructs with a nomological (i.e. law-like) character. (explanans)

What is a computational model?

TODO

What is an explanation?

In the productive explanation framework, a theory T putatively explains a phenomenon P if and only if a formal model of the theory T produces a statistical pattern representing the empirical phenomenon P.

End

Contact

CC-BY-SA 4.0